《隨機數學及其套用》是2012年出版的圖書，作者是劉國慶。本書可作為高等院校英才班本科生雙語教材，也可供相關專業研究生、廣大教師參考使用。
基本介紹
- 書名：隨機數學及其套用
- 作者：劉國慶
- ISBN：978-7-5603-3768-5
- 定價：43.80
基本信息,內容簡介,目錄,
基本信息
書名:隨機數學及其套用
作者:劉國慶 ISBN:978-7-5603-3768-5
責任編輯:孫傑 出版時間:2012.8
本社類別:I.數/理/化/力學/生物/動力工程能工程熱物理類
所屬叢書:無
開本:16 定價:43.80
折扣價:43.8
內容簡介
隨機數學是數學的重要分支之一。本書涉及隨機事件、機率公理、全機率公式、貝葉斯公式、隨機變數及其分布、二維變數的聯合分布、數學期望、條件期望、大數定律、數理統計等內容。本書提供了處理截尾變數均值與方差的半參數界的方法。本書可為廣大讀者在機率論、高斯過程、小值機率、Stein方法、矩問題等領域進一步學習提供必要的知識儲備。
目錄
Chapter 1 Events and Probability
1.1 Events as Sets
1.2 Probability
1.3 Exercises
Chapter 2 Random Variables and Their Distributions
2.1 Random Variables
2.2 Discrete Random Variables
2.3 Expected Value of Discrete Random Variable
2.4 Expectation of a Function of a Discrete Random Variable
2.5 Variance of Random Variables
2.6 Continuous Random Variables
2.7 Distribution of a Function of a Random Variable
2.8 Exercises
Chapter 3 Joint Distributions of Two Random Variables
3.1 Joint Cumulative Probability Distribution Function
3.2 Joint Probability Mass Function for Discrete Random Variable
3.3 Joint Probability Density Function
3.4 Independent Random Variables
3.5 Covariance
3.6 Correlation Coefficient
3.7 Bivariate Normal Distribution
3.8 Conditional Distributions
3.9 Joint Probability Distribution of Functions of Random Variables
3.10 Exercises
Chapter 4 Law of Large Numbers
4.1 Generating Functions and Their Applications
4.2 Characteristic Functions
4.3 Limit Theorems
4.4 Law of Large Numbers (LLN)
4.5 Exercises
Chapter 5 Mathematical Statistics
5.1 Introduction
5.2 Random Sampling
5.3 Distributions of Statistics
5.4 The Sample Mean and the Sample Variance
5.5 Point Estimation
5.6 Confidence Intervals
5.7 Testing of Hypotheses
5.8 Exercises
Chapter 6 Approaches to Semiparametric Bounds on Means and Variances
6.1 Introduction to Moment Problems
6.2 Convex Optimization Approach (Duality Theory)
6.3 Semidefinite Programming(SDP)
6.4 Khinchin Transform Method for Unimodal Distributions
6.5 Convex Representation
6.6 Symmetrization Methods for Variance
6.7 Optimal Distance and Optimal Ratio
6.8 Other Methods
Index
後記
